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Gradient Functions

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New words: Differentiation, derivative New notation: New process: Differentiating a function New knowledge: When and why to differentiate a function

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Gradient of...... Equation of this line......

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Gradient of a Curve?

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Can you see any connection between the gradient of x 2 (shown by the tangents) and different x values.connection

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22x is the same as 2x 1 22x 1 times by power 2x 1 22x 1 take 1 from power 2x 0 = 2(1)=2 FFor ax the derivative is just a 33 is the same as 3(x 0 ) 33x 0 times by power 0x3x 0 wwell that’ll be 0 then. 1 minute

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Just differentiate one term at a time. E.g. y = 5x 3 – 2x 2 + 4x – 3 Try f(x) = 7x 3 + 6x 2 – 9x - 5 1 minute

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You have 32 problems to solve You may work alone or in pairs – but your scores go towards the table total 1 point for each problem solved Once checked crumple and toss – 1 or 2 points for getting it in the bin! 96 points on offer

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Write the gradient formula for the following... 1) y = x 2 – x8) f(x) = 2 – 3x 2 2) y = 4x 2 9) f(x) = 4x 3 – 5x 2 + 2 3) y = 3x 2 – 2x10) f(x) = 7x 3 – 6x + 4x 2 4) y = 2 – 3x11) f(x) = 2x 4 – 5x 2 + 3x 5) y = x – 2 – 2x 2 12) f(x) = 9 6) y = 2 + 4x – 3x 2 13) 9x 7 – 4x 5 + 3x 2 7) y = 3x – 114) 8x 3 – 5x 4 + 8x 2 + 3x

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